{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "google",
   "metadata": {},
   "source": [
    "##### Copyright 2025 Google LLC."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "apache",
   "metadata": {},
   "source": [
    "Licensed under the Apache License, Version 2.0 (the \"License\");\n",
    "you may not use this file except in compliance with the License.\n",
    "You may obtain a copy of the License at\n",
    "\n",
    "    http://www.apache.org/licenses/LICENSE-2.0\n",
    "\n",
    "Unless required by applicable law or agreed to in writing, software\n",
    "distributed under the License is distributed on an \"AS IS\" BASIS,\n",
    "WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
    "See the License for the specific language governing permissions and\n",
    "limitations under the License.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "basename",
   "metadata": {},
   "source": [
    "# golomb_sat"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "link",
   "metadata": {},
   "source": [
    "<table align=\"left\">\n",
    "<td>\n",
    "<a href=\"https://colab.research.google.com/github/google/or-tools/blob/main/examples/notebook/examples/golomb_sat.ipynb\"><img src=\"https://raw.githubusercontent.com/google/or-tools/main/tools/colab_32px.png\"/>Run in Google Colab</a>\n",
    "</td>\n",
    "<td>\n",
    "<a href=\"https://github.com/google/or-tools/blob/main/examples/python/golomb_sat.py\"><img src=\"https://raw.githubusercontent.com/google/or-tools/main/tools/github_32px.png\"/>View source on GitHub</a>\n",
    "</td>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "doc",
   "metadata": {},
   "source": [
    "First, you must install [ortools](https://pypi.org/project/ortools/) package in this colab."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "install",
   "metadata": {},
   "outputs": [],
   "source": [
    "%pip install ortools"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "description",
   "metadata": {},
   "source": [
    "\n",
    "This is the Golomb ruler problem.\n",
    "\n",
    "This model aims at maximizing radar interferences in a minimum space.\n",
    "It is known as the Golomb Ruler problem.\n",
    "\n",
    "The idea is to put marks on a rule such that all differences\n",
    "between all marks are all different. The objective is to minimize the length\n",
    "of the rule.\n",
    "see: https://en.wikipedia.org/wiki/Golomb_ruler\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "code",
   "metadata": {},
   "outputs": [],
   "source": [
    "from typing import Sequence\n",
    "from ortools.sat.colab import flags\n",
    "from google.protobuf import text_format\n",
    "from ortools.sat.python import cp_model\n",
    "\n",
    "_ORDER = flags.define_integer(\"order\", 8, \"Order of the ruler.\")\n",
    "_PARAMS = flags.define_string(\n",
    "    \"params\",\n",
    "    \"num_search_workers:16,log_search_progress:true,max_time_in_seconds:45\",\n",
    "    \"Sat solver parameters.\",\n",
    ")\n",
    "\n",
    "\n",
    "def solve_golomb_ruler(order: int, params: str) -> None:\n",
    "    \"\"\"Solve the Golomb ruler problem.\"\"\"\n",
    "    # Create the model.\n",
    "    model = cp_model.CpModel()\n",
    "\n",
    "    var_max = order * order\n",
    "    all_vars = list(range(0, order))\n",
    "\n",
    "    marks = [model.new_int_var(0, var_max, f\"marks_{i}\") for i in all_vars]\n",
    "\n",
    "    model.add(marks[0] == 0)\n",
    "    for i in range(order - 2):\n",
    "        model.add(marks[i + 1] > marks[i])\n",
    "\n",
    "    diffs = []\n",
    "    for i in range(order - 1):\n",
    "        for j in range(i + 1, order):\n",
    "            diff = model.new_int_var(0, var_max, f\"diff [{j},{i}]\")\n",
    "            model.add(diff == marks[j] - marks[i])\n",
    "            diffs.append(diff)\n",
    "    model.add_all_different(diffs)\n",
    "\n",
    "    # symmetry breaking\n",
    "    if order > 2:\n",
    "        model.add(marks[order - 1] - marks[order - 2] > marks[1] - marks[0])\n",
    "\n",
    "    # Objective\n",
    "    model.minimize(marks[order - 1])\n",
    "\n",
    "    # Solve the model.\n",
    "    solver = cp_model.CpSolver()\n",
    "    if params:\n",
    "        text_format.Parse(params, solver.parameters)\n",
    "    solution_printer = cp_model.ObjectiveSolutionPrinter()\n",
    "    print(f\"Golomb ruler(order={order})\")\n",
    "    status = solver.solve(model, solution_printer)\n",
    "\n",
    "    # Print solution.\n",
    "    if status in (cp_model.OPTIMAL, cp_model.FEASIBLE):\n",
    "        for idx, var in enumerate(marks):\n",
    "            print(f\"mark[{idx}]: {solver.value(var)}\")\n",
    "        intervals = [solver.value(diff) for diff in diffs]\n",
    "        intervals.sort()\n",
    "        print(f\"intervals: {intervals}\")\n",
    "    print(solver.response_stats())\n",
    "\n",
    "\n",
    "def main(argv: Sequence[str]) -> None:\n",
    "    if len(argv) > 1:\n",
    "        raise app.UsageError(\"Too many command-line arguments.\")\n",
    "    solve_golomb_ruler(_ORDER.value, _PARAMS.value)\n",
    "\n",
    "\n",
    "main()\n",
    "\n"
   ]
  }
 ],
 "metadata": {
  "language_info": {
   "name": "python"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
